Multiplication

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Multiplication | Multiplying by 10, 100, 1000... | Long multiplication | Grid multiplication | Gelosia or Lattice

Multiplication

Multiplication is usually associated with the idea of repeated addition, e.g.
7 x 6 = 6 + 6 + 6 + 6 + 6 + 6 + 6 = 42

Students should know their 12 times table competently and be able to recognise the equivalence of different multiplications, e.g.
8 x 7 = 56
7 x 8 = 56
Multiply table.PNG
In terms of common methods, students will have encountered many different techniques for helping them to calculate multiplications. They should be confident with their own way, but understand the commonality between methods.
Multiplication | Multiplying by 10, 100, 1000... | Long multiplication | Grid multiplication | Gelosia or Lattice

Multiplying by 10, 100, 1000...

Normally in mathematics, students will be encouraged to fix the decimal point and place value holders and move the digits left or right when multiplying or dividing by 10 respectively. This reinforces the importance of place value and is used commonly in the teaching of standard index form
Multiply 10.PNG

Multiplication | Multiplying by 10, 100, 1000... | Long multiplication | Grid multiplication | Gelosia or Lattice

Long multiplication

This may be the multiplication method you are most familiar with. It is common for students to blindly follow some algorithm to complete this method, often not understanding what they are doing.

Standard method – long multiplication
24
x 16
144 (6 x24)
240 (10 x 24)
384
Long multiply.PNG

Multiplication | Multiplying by 10, 100, 1000... | Long multiplication | Grid multiplication | Gelosia or Lattice

Grid multiplication

It is common for students to be taught this method of multiplication at primary schools. It reinforces the multiplication of every place value, and forms the basis of subsequent methods for expanding and factorising alegraic expressions. Each number is split into place value parts and then added to the grid. The number of individual multiplications is therefore increased, but each calculation is more straightforward.

Find 87 x 63

  1. Step 1 Partition into tens and units and arrange the numbers on a grid. 87 = 80 + 7 and 63 = 60 + 3
  2. Step 2 In each box write the product.
  3. Step 3 Add together the numbers in the boxes. The total is the product of 87 and 63
Grid.PNG

Calculate 327 x 53

Estimate: 300 x 50 = 15 000

X
 300
 20
 7
 Total
50
 15 000
 1000
 350
 16 350
3
 900
 60
 21
 981
Total
 15900
 1060
 371
 17331

Multiplication | Multiplying by 10, 100, 1000... | Long multiplication | Grid multiplication | Gelosia or Lattice

Gelosia or Lattice

There are many ways to do long multiplication. This method for multiplication is called the lattice method or Gelosia. To multiply 149 by 87, follow these steps;
  1. Step 1 Estimate 149 x 87 ≈ 150 x 90 = 13 500
  2. Step 2 Draw a grid (see below)
  3. Step 3 Fill in the squares. Each time multiply the number at the top by the one at the side. For example 9 x 8 = 72 and 4 x 7 = 28
  4. Step 4 Add diagonally
Gelosia.PNG

Multiplication | Multiplying by 10, 100, 1000... | Long multiplication | Grid multiplication | Gelosia or Lattice